# Closure, Interior and limit points of finite compliment topology question

• Apr 8th 2009, 04:28 PM
monkey.brains
Closure, Interior and limit points of finite compliment topology question
Hey

I was wondering if someone could help me out with the following question.

Let U be any open set in the finite complement topology on $\displaystyle \Re$.

(a)Describe the Cl(U), Int(U) and $\displaystyle \mathfrak{d}$(U)

(b) What is the set of limit points of U
• Apr 8th 2009, 10:14 PM
aliceinwonderland
Quote:

Originally Posted by monkey.brains
Hey

I was wondering if someone could help me out with the following question.

Let U be any open set in the finite complement topology on $\displaystyle \Re$.

(a)Describe the Cl(U), Int(U) and $\displaystyle \mathfrak{d}$(U)

(b) What is the set of limit points of U

(a) Cl(U) = R, Int(U) = U,
$\displaystyle \mathfrak{d}$$\displaystyle (U) = \bar{U} \cap \overline{R\setminus U}, Since U is an open set, \displaystyle \mathfrak{d}(U) = \displaystyle \overline{R\setminus U} = R \setminus U. (b)The limit points of U are all points in R. • Apr 10th 2009, 02:47 PM monkey.brains Quote: Originally Posted by aliceinwonderland (a) Cl(U) = R, Int(U) = U, \displaystyle \mathfrak{d}$$\displaystyle (U) = \bar{U} \cap \overline{R\setminus U}$,
Since U is an open set, $\displaystyle \mathfrak{d}$(U) = $\displaystyle \overline{R\setminus U} = R \setminus U$.
(b)The limit points of U are all points in R.

hey could you please clarify what does the line over R minus U means??
• Apr 10th 2009, 02:53 PM
Plato
Quote:

Originally Posted by monkey.brains
hey could you please clarify what does the line over R minus U means??

Often $\displaystyle \overline{A}$ stands for the closure of $\displaystyle A$.